Chapter 11.2, Problem 44E

### Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

Chapter
Section

### Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

# Determine whether the series is convergent or divergent by expressing s n as a telescoping sum (as in Example 8). If it is convergent, find its sum. ∑ n = 1 ∞ ln n n + 1

To determine

The series is convergent or divergent by expressing sn as a telescoping sum and if it is convergent, find its sum.

Explanation

1) Concept:

Use the definition to determine whether the series is convergent or divergent by expressing sn as telescoping sum and find the sum of series.

2) Definition:

A series n=1an=a1+a2+a3+, let sn denote its nth partial sum

sn=i=1nai=a1+a2+a3++an

If the sequence {sn} is convergent and limnsn=s exists as a real number, then the series an is called convergent and written as

a1+a2+a3++an+=s

The number s is called the sum of the series.

If the sequence {sn} is divergent, then the series an is called divergent.

3) Given:

n=1lnnn+1

4) Calculation:

Consider

n=1lnnn+1

The given series can be wr

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